Qualitative theory of multi-scale dynamical systems and applications (R-8709)

Dynamical systems with different scales are systems of differential equations, whose solutions simulate the dynamics in models where slow activities interact with fast activities, think for example of the slowly changing climate vs the daily weather changes, or for example the acute voltage spike of a neuron as compared to the relatively long silent phase of the neuron. In this project we elaborate techniques on how to reduce such multi-scale dynamical systems to its simplest form (a normal form) that ideally can be integrated exactly, we discuss the effect of noise and we finally focus our attention on a phenomenon - bifurcation delay - triggered in analytic models while absent in smooth models.

Keywords:bifurcation delay,, NORMAL FORMS, singular perturbations

Disciplines:Analysis